Arnold Diffusion in a priory chaotic Hamiltonian systems

Abstract

We assume that a symplectic real-analytic map has an invariant normally hyperbolic cylinder and an associated transverse homoclinic cylinder. It is well known that such cylinder is preserved under small perturbations. We prove that for a generic real- analytic perturbation of this map the boundaries of the cylinder are connected by trajectories of the perturbed map.

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